JEE Main 2023MathematicsSequences and SeriesHardNumerical

JEE Main 2023 — Sequences and Series Question with Solution

JEE Main 2023 (01 Feb Shift 2)

Question

The sum of the common terms of the following three arithmetic progressions.

3,7,11,15,…………,399

2,5,8,11,.........359  and

2,7,12,17,……,197, is equal to _____ .

Enter your answer

Show full solutionCorrect answer: 321
Correct answer
321

Step-by-step explanation

We have,

S1: 2,5,8,11,...,359

Common difference is d1=3

S2: 3,7,11,15...,399

Common difference is d2=4

S3:2,7,12,17...,197

Common difference is d3=5

Now taking LCM of common difference we get,

LCMd1, d2, d3=60

So, common terms are 47,107,167,

Hence, the sum will be 47+107+167=321.

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About this question

This is a previous-year question from JEE Main 2023, covering the Sequences and Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.